Student[Calculus1][ExtremePoints] - find the extreme points of an expression

Calling Sequence

ExtremePoints(f(x), x, opts)

ExtremePoints(f(x), x = a..b, opts)

ExtremePoints(f(x), a..b, opts)

Parameters

f(x)

-

algebraic expression in variable 'x'

x

-

name; specify the independent variable

a, b

-

algebraic expressions; specify restricted interval for extreme points

opts

-

equation(s) of the form numeric=true or false; specify computation options

Description

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The ExtremePoints(f(x), x) command returns all extreme points of f(x) as a list of values.

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The ExtremePoints(f(x), x = a..b) command returns all extreme points of f(x) in the interval [a,b] as a list of values.

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If the independent variable can be uniquely determined from the expression, the parameter x need not be included in the calling sequence.

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An extreme point is defined as any point which is a local minimum or maximum, which includes any finite end points.

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If the expression has an infinite number of extreme points, a warning message and sample extreme points are returned.

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The opts argument can contain the following equation that sets computation options.

numeric =true or false

Whether to use numeric methods (using floating-point computations) to find the extreme points of the expression. If this option is set to true, the points a and b must be finite and are set to and if they are not provided. By default, the value is false.